Mathematical Modeling of Storm Surge in Three … · Mathematical Modeling of Storm Surge in Three Dimensional Primitive Equations ... Wannawong et al. ... (vsinφ−wcos φ) reduces

Mathematical Modeling of Storm Surge in ThreeDimensional Primitive Equations

Worachat Wannawong∗, Usa W. HumphriesPrungchan Wongwises and Suphat Vongvisessomjai

Abstract—The mathematical modeling of storm surge in sea andcoastal regions such as the South China Sea (SCS) and the Gulf ofThailand (GoT) are important to study the typhoon characteristics.The storm surge causes an inundation at a lateral boundary exhibitingin the coastal zones particularly in the GoT and some part of the SCS.The model simulations in the three dimensional primitive equationswith a high resolution model are important to protect local propertiesand human life from the typhoon surges. In the present study, themathematical modeling is used to simulate the typhoon–inducedsurges in three case studies of Typhoon Linda 1997. The resultsof model simulations at the tide gauge stations can describe thecharacteristics of storm surges at the coastal zones.

Keywords—lateral boundary, mathematical modeling, numericalsimulations, three dimensional primitive equations, storm surge.

I. INTRODUCTION

The numerical experiments of the mathematical modelingare designed to study the storm surges in a three dimen-

sional model. It is important to solve the primitive equationsof the surface boundary conditions by the high resolutionnumerical oceanic model.

The primitive equations are a governing equation of thePrinceton Oceanic Model (POM)[1] which is described bythe Reynold’s averaged equations of mass, momentum, tem-perature and salinity conservations. The POM model has beendeveloped to study the external gravity waves, internal gravitywaves, tidal waves, surges and currents. In 2000, it was appliedto study currents in the Gulf of Thailand (GoT) by the RoyalThai Navy. It was also developed by the Thailand ResearchFund project in 2003 in order to study the storm–surge andeffect of tidal forcing. Wannawong et al. [14] worked onthe comparison of orthogonal curvilinear grid and orthogonalrectangular grid in the horizontal coordinates. Even thoughthe velocities of seawater current provided by the orthogonalcurvilinear grid were more acceptable in the coastal zonethan that of the orthogonal rectangular grid, the velocities ofcurrent obtained from both grids were not much different. Theorthogonal rectangular grid, therefore, was chosen to study thestorm surge and current [14].

Wannawong et al. [15], [16] also studied on the finegrid domain and reported that the storm waves and surgessignificantly influenced the wave heights and surges [17], [18].In this study, the numerical ocean predictions were presented

The authors would like to acknowledge the Commission on Higher Ed-ucation for giving financial support to Mr.Worachat Wannawong under theStrategic Scholarships Fellowships Frontier Research Networks in 2007.

∗Corresponding author, Email: [email protected].: +66 2470 8921 Fax: +66 2428 4025.

as the time series of the storm surges at ten tide gauge stationsby using the three dimensional model. The objective of thiswork is to modify the mathematical modeling which is theprimitive equations under the surface boundary condition ofthree experiments of the storm surge cases. The study domainis extended from the domain studied by Wannawong et al.[14] to the new domain studied by Wannawong et al. [16],[17] which was similar to the fine grid domain of the stormwave model [18]. Furthermore, the mathematical modelingis modified to study the storm surge cases with the timeseries of Typhoon Linda 1997 by the POM model. The studydomain covering from 99◦E to 111◦E in longitude and from2◦N to 14◦N in latitude with high resolution 0.1◦ × 0.1◦

is modified to three experiments: 2D–barotropic mode, 3D–baroclinic mode in the prognostic option and 3D–baroclinicmode in the diagnostic option. The experiments are simulatedin the study domain by the POM model as illustrated in Fig.1. The outline of this study is organized as follows: SectionII gives a brief description of the three dimensional primitiveequations and its modifications to the study domain; SectionIII presents the model parameters and numerical experiments;Section IV shows the results of experiments; and Section Vpresents the discussions and also conclusion.

II. THE THREE DIMENSIONAL PRIMITIVE EQUATIONS

AND ITS MODIFICATIONS

The mathematical modeling of storm surges used in thisstudy has been modified and described in this section. Thethree dimensional primitive equations and its modificationswere developed from the Princeton Oceanic Model (POM) [1]in order to simulate surges, inundations, currents and coastalcirculations. In this section, a brief description of the modelapplied in the study domain is presented in the followingsections.

A. The Three Dimensional Primitive Equations

The governing equation of the three dimensional model canbe exhibited in the orthogonal Cartesian coordinate systemswhich includes the Reynold’s averaged equations of mass, mo-mentum, temperature and salinity conservations. The equationsnot only indicate the effect of the gravitational/buoyancy forcesbut the effect of the Coriolis pseudo–force is also expressed.The equations can be written as follows.

Continuity equation:

∂u

∂x+

∂v

∂y+

∂w

∂z= 0, (1)

World Academy of Science, Engineering and TechnologyInternational Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Vol:5, No:6, 2011

797International Scholarly and Scientific Research & Innovation 5(6) 2011 scholar.waset.org/1999.7/6330

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http://waset.org/publication/Mathematical-Modeling-of-Storm-Surge-in-Three-Dimensional-Primitive-Equations/6330

http://scholar.waset.org/1999.7/6330

x–momentum equation:

du

dt= − 1

ρ◦∂p

∂x+ fv +

∂

∂z(Amv

∂u

∂z) + Fx, (2)

y–momentum equation:

dv

dt= − 1

ρ◦∂p

∂y− fu +

∂

∂z(Amv

∂v

∂z) + Fy, (3)

z–momentum or hydrostatic equation:

∂p

∂z= −ρg, (4)

Temperature equation:

dT

dt=

∂

∂z(Ahv

∂T

∂z) + FT , (5)

Salinity equation:

dS

dt=

∂

∂z(Ahv

∂S

∂z) + FS , (6)

The terms d(·)/dt, Fx, Fy , FT and FS presented in theequations (2), (3), (5) and (6) represent the total derivativeterms, these unresolved processes and in analogy to themolecular diffusion can be described as

Fx =∂

∂x

[2Am

∂u

∂x

]+

∂

∂y

[Am

(∂u

∂y+

∂v

∂x

)],

Fy =∂

∂y

[2Am

∂v

∂y

]+

∂

∂x

[Am

(∂u

∂y+

∂v

∂x

)],

and

FT,S =∂

∂xAh

∂(T, S)∂x

+∂

∂yAh

∂(T, S)∂y

.

where u, v are the horizontal components of the velocityvector, w is the vertical component of the velocity vector,g is the gravitational acceleration, p is the local pressure,ρ(x, y, z, t, T, S) is the local density, ρ◦ is the reference waterdensity, Am is the horizontal turbulent diffusion coefficient,Amv is the vertical turbulent diffusion coefficient, f = 2Ω sinφis the Coriolis parameter where Ω is the speed of angularrotation of the earth by Ω = 7.2921× 10−5 rad s−1 and φ isthe latitude, T is the potential temperature, S is the potentialsalinity, Ah is the horizontal thermal diffusivity coefficient,Ahv is the vertical thermal diffusivity coefficient, the termsFx and Fy are the horizontal viscosity terms and the termsFT and FS are the horizontal diffusion terms of temperatureand salinity respectively.

The main assumptions used in the derivation of above equa-tions are that: (a) the water is incompressible (dρ/dt = 0); (b)the density differences are small and can be neglected, exceptin buoyant forces (Boussinesq approximation). Consequently,the density ρ◦ used in the x and y momentum equations (2)and (3) is a reference density that is either represented by thestandard density of the water or by the depth averaged waterdensity as follows:

ρ◦ =1

η + h

∫ η

−h

ρdz =1D

∫ η

−h

ρdz (7)

where the total depth D is expressed as: D = η + h that is,the sum of the sea surface elevation η above the mean sea

level (MSL) plus the depth h of the still water level. Thedensity ρ used in the z–momentum is represented by the sumof the reference density ρ◦ and its variation ρ′(ρ = ρ◦ + ρ′).The last assumption (c) is that, the vertical dimensions aremuch smaller than the horizontal dimensions of the water fieldand the vertical motions are much smaller than the horizontalones. Consequently, the vertical momentum equation reducesto the hydrostatic law (hydrostatic approximation) and theCoriolis term 2Ω(v sin φ−w cosφ) reduces to 2Ωv sin φ (seethe equation (2)). The vertical integration of the equation (4)from the depth z to the free surface η yields the pressure atthe water depth z as:

p|η − p|z = g

∫ η

z

ρdz′ −→

p = patm + gρ◦(η − z) + g

∫ η

z

ρ′dz′ (8)

where z′ is a dummy variable for integration, η is the seasurface elevation above the MSL, p|z = p = p(x, y, z, t) andp|η = patm is the standard atmospheric pressure.

It is necessary to state the relationship of the water density,temperature and pressure in order to close the above systemof the continuity and motion equations. This relationship inPOM model is coded by the following formulation proposedby Mellor [2], that approximates the more general, and alsomore computationally expensive. The formulations of theInternational Equation of State (UNESCO) are given below.

ρ(S, T, p) = ρ(S, T, 0) +p

c2(1 − 0.20

p

c2) · 104 (9)

c(S, T, p) = 1449.2 + 1.34(S − 35) + 4.55T − 0.045T 2

+ 0.00821p + 15.0 · 10−9p2 (10)

where T is the temperature, p is the gage pressure, S is thesalinity and c is the sound speed.

B. Boundary conditions

1) Surface boundary conditions: The continuity, momen-tum and temperature surface boundary conditions describe theinteraction of the water surface with the atmosphere. They aredefined as:

w|η =

[∂η

∂t+ u

∂η

∂x+ v

∂η

∂y

]η

(11)

Amv

[∂u/∂z

∂v/∂z

]η

=[τsx/ρ◦τsy/ρ◦

](12)

T = ρ◦Ahv∂T

∂z

∣∣∣∣η

(13)

S = ρ◦Ahv∂S

∂z

∣∣∣∣η

(14)

The equation (11) represents the surface boundary conditionfor the continuity equation (1), as expressed by the kinematicfree surface condition. At free surface, the kinematic boundarycondition can be derived considering the fact that the freesurface is a material boundary for which a particle initiallyon the boundary will remain on the boundary. Assuming that



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there is no water penetrating the free surface, then the materialor total derivative at the free surface (η−z) is zero, therefore:

D(η − z)Dt

=Dη

Dt− Dz

Dt= 0 =⇒[

∂η

∂t+ u

∂η

∂x+ v

∂η

∂y+ w

∂η

∂z

]η

−[

∂z

∂t+ u

∂z

∂x+ v

∂z

∂y

+w∂z

∂z

]z

= 0 (15)

Since, ∂η/∂z = ∂z/∂t = ∂z/∂x = ∂z/∂y = 0 and ∂z/∂z =1, the equation (15) reduces to the equation (11).

The equation (12) represents the surface boundary conditionfor the z–momentum or the hydrostatic equation (4) with thesurface wind stresses given by the drag law (bulk formula) as:[

τsx

τsy

]= ρairCMW

[Wx

Wy

]; τs = ρairCM |W |W ;

W =(W 2

x + W 2y

)1/2(16)

where W is the wind speed at 10 m above the sea watersurface, Wx and Wy are two components of the wind speedvector, ρair is the density of air at the standard atmosphericconditions, CM is the bulk momentum transfer (drag) coeffi-cient and τs is the wind imposed surface stress.

The drag coefficient (CM ) is assumed to vary with the windspeed as:

103CM =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

2.5 if |W | > 22 m s−1

0.49 + 0.065|W | if 8 ≤ |W | ≤ 22 m s−1

1.2 if 4 ≤ |W | < 8 m s−1

1.1 if 1 ≤ |W | < 4 m s−1

2.6 if |W | < 1 m s−1

0.63 + 0.066|W | for all |W |0.63 + (0.066|W |2)1/2 for all |W |.

This CM formula follows Large and Pond [13] when thewind speed is less than 22 m s−1; otherwise, it is assumed tobe a constant as indicated in Powell et al. [4]. The equations(13) and (14) represent the surface boundary condition forthe temperature and salinity equations (see the equations (15)and (16)). T represents the net surface heat flux and S ≡S(0)[E− P ]/ρ◦ where (E− P ) represents the net evaporationE – precipitation P fresh water surface mass flux rate andS(0) represents the surface salinity.

2) Bottom boundary conditions:

w|−h = −[u

∂h

∂x+ v

∂h

∂y

]−h

(17)

Amv

[∂u/∂z

∂v/∂z

]−h

=[τbx/ρ◦τby/ρ◦

](18)

ρ◦Ahv∂T

∂z

∣∣∣∣−h

= 0 (19)

ρ◦Ahv∂S

∂z

∣∣∣∣−h

= 0 (20)

The equation (17) represents the bottom boundary conditionfor the continuity equation (1), as expressed by the kinematic

boundary condition. At the bottom, the kinematic boundarycondition reflects the fact that there is no flow normal to theboundary, therefore, the material derivative z + h is zero:

D(z + h)Dt

=Dz

Dt+

Dh

Dt= 0 =⇒[

∂z

∂t+ u

∂z

∂x+ v

∂z

∂y+ w

∂z

∂z

]−h

+

[∂h

∂t+ u

∂h

∂x+ v

∂h

∂y

+w∂h

∂z

]−h

= 0 (21)

and since, ∂z/∂t = ∂h/∂t = ∂z/∂x = ∂z/∂y = ∂h/∂z = 0and ∂z/∂z = 1, the equation (21) reduces to the equation(17).

The equation (18) represents the bottom boundary conditionfor the z–momentum or the hydrostatic equation (4). Thebottom shear stresses are parameterized as follows:[

τbx

τby

]= ρ◦CD|u|

[u

v

]; τb = ρ◦CD|u|u ;

|u| =(u2 + v2

)1/2(22)

where u and v are the horizontal flow velocities at the gridpoint closest to bottom and CD is the bottom drag coefficientdetermined as the maximum between a value calculated ac-cording to the logarithmic law of the wall and a value equalto 0.0025:

CD = max

[k2

(ln

h + zb

z◦

)−2

, 0.0025

](23)

where z◦ is the bottom roughness height in the presentapplication z◦ = 1 cm, zb is the grid point closest to bottom,and k = 0.4 is the von Karman’s constant. In the 2D barotropicmode of the POM model, CD is shown as 0.0025.

On the side walls and bottom of the gulf, the normalgradients of T and S in the equations (19) and (20) are zero.Therefore, there are no advective and diffusive heat and saltfluxes across these boundaries.

3) Lateral boundary conditions: The GoT is modeled asa closed gulf without inflow or outflow from the gulf rivers.Consequently, the lateral conditions for the wall boundary arespecified that: (a) there is no flow normal to the wall (∂un/∂n= 0), and (b) the no slip conditions tangential to the wall arevalid (uτ = 0), where u represents the velocity vector, and nand τ are the normal and tangential directions.

C. Wind stress and atmospheric pressure conditions

The typhoon pressure field and surface wind velocity createdby the pressure gradient were modeled following the Bowden[3] and Pugh [10] relationships:

∂pair

∂η= −ρg, (24)

∂η

∂x=

ρairCMW 2

ρgD. (25)

where pair is the atmospheric pressure, η is the sea surfaceelevation from the reference level of undisturbed surface, ρ



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is the density of sea water in the z–momentum, g is thegravitational acceleration of the earth, x is the coordinate inthe east–west direction, ρair is the density of air, CM is thedrag coefficient, W is the wind profile that results from thetyphoon pressure gradient and D is the total depth of sea water.According to the equation (24), the pressure reducing for 1 mbcorresponds to about a 1 cm rise in the sea level. The totalwater depth D inversely affects the sea surface elevation η,whereas the wind speed at the specific height (10 m) directlyaffects the sea surface elevation.

For the POM model, the computational stability conditionon the external and internal modes was described by Worachatet al. [16], [17]. The stability of both models was computedaccording to the Courant–Friedrichs–Lewy (CFL) stabilitycondition. For more details of the sensitivity of the POMmodel to the time steps, see Ezer et al. [11].

III. THE MODEL PARAMETERS AND NUMERICAL

EXPERIMENTS

A. The Bathymetry of the Study Domain

The bathymetry of the study domain is defined by theshoreline, bathymetry and specified transfer boundaries. Insome parts of the SCS and GoT, the computations of the modeltake place on a 0.1◦ × 0.1◦ rectangular grid in the horizontalcoordinate and on a sigma layer in the vertical coordinatewith 21 layers. The domain covered from 99◦E to 111◦E inlongitude and from 2◦N to 14◦N in latitude. The shorelineand bathymetry of the GoT on the 0.1◦ × 0.1◦ grid showedin Fig. 1 were obtained from GEODAS (available onlinefrom http://www.ngdc.noaa.gov/mgg/gdas). The original ver-sion (1993) of ETOPO5 [5], on a 5–minute latitude/longitudegrid (1 minute of latitude = 1 nautical mile, or 1.853 km) wasupdated in June 2005 for the acceptably deep water.

B. Model Initialization and Forcing

The model is initialized by setting the velocity, temperatureand salinity fields to be zero. These sets known as “cold start”requires the model run for spin up period before it reaches astate of statistical equilibrium. In the present application, thetyphoon spin up period was adequate for the model to reachequilibrium and to provide the realistic results.

The forcing of model during the spin up period and thesubsequent model simulations require the use of the followingmeteorological data: temperature, salinity, sea level pressure,wind speed and direction. The wind and pressure fields wereobtained from the U.S. Navy Global Atmospheric PredictionSystem (NOGAPS) which is a global atmospheric forecastingmodel with 1◦×1◦ data resolution (Hogan and Rosmond [12];Harr et al. [6]). The temperature and salinity with 1◦ × 1◦

data resolution provided by Levitus94 (Levitus and Boyer [8];Levitus et al. [7]) were indicated by the climatological monthlymean fields in the model. The high resolution of 0.1◦ × 0.1◦

spatial grid size gave 121 × 121 points by using the bilinearinterpolation of these data in the horizontal coordinate. Inthe vertical coordinate, 21 sigma levels were employed foradequacy and computational efficiency. The model time stepswere 20 s and 1200 s (20 min) for the external and internal

time steps respectively.The horizontal momentum equations consist of the local

time derivative and horizontal advection terms, Coriolis de-flection, sea level pressure gradient, tangential wind stress onthe sea surface, and quadratic bottom friction. The system ofequations is written in the flux form and solved by using thefinite differential method that is centered in time and space onthe Arakawa C grid. Finally, the results of the POM modelwere correspondingly represented in every hour of TyphoonLinda 1997 entering into some parts of the SCS and GoT.The stability of the model was computed according to theCFL stability condition.

C. Experimental Designs

Three experiments were performed in this study in order tocompute the storm surge on the sea surface layer (Table 1).In this study, the storm surge applications of the POM modelwhich is one of the three dimensional model was studied. ThePOM model was run by considering the difference between 2Dand 3D modes with the time series. The model simulationswere conducted by using the 2D mode of the POM modelas the primary objectives which were to study the barotropicwater level variation and volume exchange. To test the ade-quacy of the POM model, the 2D and 3D modes were testedas described by Blumberg and Mellor [1].

IV. RESULTS OF EXPERIMENTS

The simulations of storm surge were calculated from a setof three dimensional model experiments: Exp. I, Exp. II andExp. III as described in Table I.

The storm surge generated by Typhoon Linda was firstlyconsidered (Exp. I) and computed by using the POM modelas presented in Fig. 4. The Bowden [3] and Pugh [10]relationships were used to describe the storm surges relatedto the strong wind and low pressure (Figs. (2)–(6)). The POMmodel using in the three experiments was run with the samewind field (wind speed), pressure field (sea level pressure),domain (wind fetch) and also the same time (duration) butwith the different computational options. Fig. (5) illustratedthe storm surges at the same location and time with thedifferent optional calculation in Exp. II. In Exp. III (see Fig.(6)), the difference of optional calculation on the sea surfacelayer can be easily considered in Figs. (4)–(6), which showedthat the storm surge increased the setup and slowed down thedifference of water recession in 2D and 3D calculations.

The effects of the extreme storm surge and the differencebetween the maximum storm surges computed by the POMmodel at ten locations of the tide gauge stations at border ofthe GoT region (Fig. 1(a) and Table II) were calculated. Thedifferences of storm surges at each station were presented inTable III in [16]. The results showed that the storm surges ateach station of all experiments presented the similar valuesand also expressed the similar trends with the observationaldata, except for those of the stations S5, S6 and S8 [16], [17].The time series of the results at ten tide gauge stations of threedimensional model showed in Figs. (7) and (8).



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V. DISCUSSIONS AND CONCLUSION

The comparisons of storm surges on the sea surface layerof the three experiments (Figs. (7) and (8)) in TyphoonLinda cases exhibited that the storm surge played a moresignificant role in determining the computations for the threedimensional primitive equations by the mathematical modeling(POM model). The role of storm surge without the storm tideunder the assumption of negligent tide forcing was presentedin this study. The slight differences of storm surges betweenExp. I, Exp. II, Exp. III and the observational data of thetyphoon distributions during Typhoon Linda entering into theGoT are shown in Figs. (7)–(8).

The results of the model can be considered that the 3D–baroclinic mode increased the setup and slowed down thewater recession, thus improving the model performance duringthe water level declining period while over predicted surgeduring the water level rising period. Since the specificationof the bottom boundary condition depends on the assumptionof the vertical velocity profile, the treatments of boundarycondition in 2D and 3D modes are not identified, whichresulted in the slight different results. The results of this workindicated that the 3D mode did not give the better resultscompared to the baseline simulation without an additionalcalibration of the 3D mode case, but the differences are notsignificant.

For the vertically integrated sea surface elevation calculatedby the POM model, the numerical experiments using thestorm surge model in the 3D prognostic and 3D diagnosticmodes have been performed. In the prognostic mode, themomentum equations as well as the temperature and salinitydistributions of the governing equation were integrated as aninitial condition. These predictive experiments do not alwaysreach the steady state due to the oceanic response time forthe density field can be considerable. As an alternative, diag-nostic computation was considered. Additional studies will beinvestigated in the future with a focus on how storm surgesaffect other domains in the GoT. The effects of the stormsurge on the sea surface layer should be more comprehensivelyexamined with more typhoon case simulations. Additionally,the calibration and validation of the observational data withthe harmonic analysis of tide in other models are needed [9].

ACKNOWLEDGMENTS

The authors would like to acknowledge the Commissionon Higher Education for kindly providing financial supportto Mr. Worachat Wannawong under the Strategic ScholarshipsFellowships Frontier Research Networks (CHE–PhD–THA–NEU) in 2007. The authors are grateful to the Geo–Informaticsand Space Technology Development Agency (Public Organi-zation) (GISTDA) for buoy data and documents. The authorsalso wish to thanks Cdr. Wiriya Lueangaram of the Meteoro-logical Division, Hydrographic Department, Royal Thai Navy,Sattahip, Chonburi, Thailand, for providing laboratory space.Finally, the authors are greatly indebted to Mr. Michael Willingand Miss Donlaporn Sae–tae for helpful comments on Englishgrammar and usage.

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[15] W. Wannawong, U. W. Humphries, P. Wongwises, S. Vongvisessomjaiand W. Lueangaram, A numerical study of two coordinates for en-ergy balance equations by wave model, Thai Journal of Mathematics,8(2010), 197–214.

[16] W. Wannawong, U. W. Humphries, P. Wongwises, S. Vongvisessomjaiand W. Lueangaram, Numerical modeling and computation of stormsurge for primitive equation by hydrodynamic model, Thai Journal ofMathematics, 8(2010), 347–363.

[17] W. Wannawong, U. W. Humphries, P. Wongwises, S. Vongvisessomjaiand W. Lueangaram, Numerical analysis of wave and hydrodynamicmodels for energy balance and primitive equations, International Journalof Mathematical and Statistical Sciences, 4(2010), 140–150.

[18] W. Wannawong, U. W. Humphries, P. Wongwises and S. Vongvisessom-jai, Three steps of one–way nested grid for energy balance equations bywave model, International Journal of Computational and MathematicalSciences, 1(2011), 23–30.



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Worachat Wannawong received the B.Sc. degreein science–physics from Srinakharinwirot Univer-sity, Bangkok, Thailand, in 2003, and the M.Sc.and Ph.D. degrees in applied mathematics fromKing Mongkut’s University of Technology Thonburi(KMUTT), Bangkok, Thailand, in 2006 and 2010,respectively. He was with the Numerical WeatherPrediction Center, Hydrographic Department, RoyalThai Navy from 2008 to 2010. He joined the Re-gional Ocean Modeling System (ROMS) team inOctober 2008. In April 2009, a part of his work was

advised by Prof. Charitha Pattiaratchi and Prof. Krish Thiagarajan from theSchool of Environmental Systems Engineering and the School of MechanicalEngineering, University of Western Australia. In December 2009, he joinedthe workshop of the climate change project at KMUTT and Prof. ZhuJiang from the Institute of Atmospheric Physics (IAP), Chinese Academyof Sciences, Beijing University gave him many ideas to modify the stormsurge model by adjusting the drag coefficient. His research interests involvenumerical analysis, numerical weather prediction, computational mathematics,and mathematical modeling.Email: [email protected]

Usa W. Humphries received the B.Sc. degree inmathematics from Prince of Songkla University,Songkla, Thailand, in 1991, the M.Sc. degree inapplied mathematics from KMUTT, in 1994, and thePh.D. degree in applied mathematics from Univer-sity of Exeter, England, in 2000. She was a NationalResearch Council Postdoctoral Investigator with theJames Rennell Division University of Southamp-ton, Southampton, England, from November 2001to December 2002 and with the IAP, China, fromOctober 10 to November 10, 2005. She currently

is an Associate Professor with the Department of Mathematics, KMUTT.Her research interests include numerical analysis, computational mathematics,oceanic modeling and climate change.Email: [email protected]

Prungchan Wongwises received the B.Sc. (SecondHonor) degree in mathematics from ChulalongkornUniversity, Bangkok, Thailand, in 1962, and theDiplom. Math. and Dr.rer.nat. degrees in math-ematics from Technical University of Karlsruhe,Germany, in 1969 and 1974, respectively. She gotthe scholarships from the Technical University ofKarlsruhe (Deutscher Akademischer Austauschdi-enst, DAAD), University of Freiburg, University ofKassel and University of Hannover under the Ger-man Government from 1966 to 1993. She currently

is an Associate Professor with the Joint Graduate School of Energy andEnvironment, KMUTT. Her research interests include numerical analysis,computational mathematics, atmospheric modeling, oceanic modeling and airpollution modeling.Email: [email protected]

Suphat Vongvisessomjai is a Professor of Hydraulicand Coastal Engineering with the Water and Envi-ronment Expert, TEAM Consulting Engineering andManagement Co., Ltd., Thailand. He was a lecturerin the Division of Water Resources Engineering,Asian Institute of Technology (AIT), Thailand, from1968 to present and a project engineer in the DelftHydraulics Laboratory, Netherlands, in 1980. Hecurrently is a Professor and Director of RegionalEnvironmental Management Center, Thailand. Hisresearch interests include drainage and flood control,

coastal erosion and pollution, and water resources.Email: [email protected]



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TABLE ITHE DESCRIPTIONS AND REFERENCE CODES OF THE NUMERICAL

EXPERIMENTS

Experimental code Description of numerical experimentsExp.I 2D–barotropic modeExp.II 3D–baroclinic mode in the prognostic optionExp.III 3D–baroclinic mode in the diagnostic option

TABLE IITHE COMPUTATIONAL AND OBSERVATIONAL POINTS FOR THE THREE

DIMENSIONAL MODEL SIMULATIONS

Station code Station name Station point Computational pointS1 Laem Ngob 102.40◦E 12.10◦N 102.38◦E 12.08◦N

S2 Laem Sing 102.07◦E 12.47◦N 102.05◦E 12.47◦N

S3 Prasae 101.70◦E 12.70◦N 101.70◦E 12.68◦N

S4 Rayong 101.28◦E 12.67◦N 101.28◦E 12.65◦N

S5 Tha Chin 100.28◦E 13.48◦N 100.28◦E 13.45◦N

S6 Mae Klong 100.00◦E 13.38◦N 100.03◦E 13.35◦N

S7 Pranburi 99.98◦E 12.40◦N 100.10◦E 12.40◦N

S8 Hua Hin 99.97◦E 12.57◦N 99.95◦E 12.57◦N

S9 Ko Lak 99.82◦E 11.80◦N 99.84◦E 11.78◦N

S10 Sichol 99.90◦E 9.00◦N 99.92◦E 8.98◦N

(a) Ten tide gauge stations at border of the GoT

9

101

103

105

107

109

111 2

4

6

8

10

12

14

550

0

0

Latitude (N)

Longitude (E) −80

−70

−60

−50

−40

−30

−20

−10

(b) Bathymetry in the perspective view

Fig. 1. (a) The study domain and observational points, and (b) the threedimensional bathymetry (m) in the perspective view

(a) 12UTC02NOV1997

(b) 00UTC03NOV1997

(c) 12UTC03NOV1997

Fig. 2. Sea level pressures (hPa) at the sea surface layer before and afterentering into the GoT



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(a) 12UTC02NOV1997

(b) 00UTC03NOV1997

(c) 12UTC03NOV1997

Fig. 3. Wind stress and its direction before and after entering into the GoT

(a) Before

(b) After

(c) Nearshore

Fig. 4. Sea surface elevation and wind stress in the 2D–barotropic modebefore and after entering into the GoT



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(a) Before

(b) After

(c) Nearshore

Fig. 5. Sea surface elevation and wind stress in the 3D–baroclinic modewith the prognostic option before and after entering into the GoT

(a) Before

(b) After

(c) Nearshore

Fig. 6. Sea surface elevation and wind stress in the 3D–baroclinic modewith the diagnostic option before and after entering into the GoT



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0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7The storm surges of POM model and tide gauge station (S1) in Typhoon Linda 1997

Time (hr)

Sto

rm s

urg

e (

m)

Exp. IExp. IIExp. III

(a) S1

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Time (hr)

Sto

rm s

urg

e (

m)


(b) S2

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Time (hr)

Sto

rm s

urg

e (

m)


(c) S3

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Time (hr)

Sto

rm s

urg

e (

m)


(d) S4

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Time (hr)

Sto

rm s

urg

e (

m)


(e) S5

Fig. 7. Comparison of three experiments at five tide gauge stations from S1to S5

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Time (hr)

Sto

rm s

urg

e (

m)


(a) S6

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Time (hr)

Sto

rm s

urg

e (

m)


(b) S7

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Time (hr)

Sto

rm s

urg

e (

m)


(c) S8

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7The storm surges of POM model and tide gauge station (T9) in Typhoon Linda 1997

Time (hr)

Sto

rm s

urg

e (

m)


(d) S9

0 50 100 150 200−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Time (hr)

Sto

rm s

urg

e (

m)


(e) S10

Fig. 8. Comparison of three experiments at five tide gauge stations from S6to S10



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